Algebra worksheet — GCSE Foundation

1.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

2.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

3.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

4.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

5.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

6.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

7.Write down the expression that means the same as m × m × m × n.

8.Which of these statements is an equation with exactly one solution?

9.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

10.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

11.A curve has equation y = x² − 9. Which statement about its graph is correct?

12.Write down the number of terms in the expression 4x² − 7x + 3.

13.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

14.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

15.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.